“Some comedians don’t take puns seriously,” says the winner of this year’s UK Pun Championships, Masai Graham, by way of a victory speech. “So it’s good to get people who love wordplay gathered together.” But while this evening of punning at Leicester comedy festival is thoroughly enjoyable, it doesn’t solve the problem Graham diagnoses. Far from it: even this event can’t bring itself to take puns seriously. The night would be more fun still if it drilled down into what differentiates good and bad puns, what separates the gifted craftsman from the word-bending genius.

The host is Lee Nelson, AKA Simon Brodkin – not himself associated with wordplay, but a capable crowd-pleaser who throws himself into the MC role. In the first half, Brodkin moderates four head-to-head quarter finals, in which opposing punners offer up their best and worst puns, plus three one-liners each in prepared response to a topic drawn from a customised dustbin. (Tonight, every expense is spared.) The eight competitors – all male – are whittled down to five, after Brodkin declares one quarter final a dead heat. The format is then repeated to reduce the field to a final two.

It’s a straitjacket of a structure, against which some of the contestants strain. It only ever allows for isolated one-liners; no one gets to build up a routine’s worth of puns, which is a shame because sometimes half the pun fun (as with Milton Jones, say) is the dizzying sensation of one piling on top of another until your brain can’t keep up.

The highlight of the quarter-final round comes when Tony Cowards and Nigel Lovell start freestyling, improvising puns about a giant letter X that Cowards has unearthed backstage. But extempore punning isn’t part of the competition, which judges only between pre-scripted lines. That’s daft: if the organisers aspire to the excitement of Eminem’s 8 Mile, as Brodkin suggests, they should add an off-the-cuff round immediately. Writing a neat pun is an estimable skill, but so is improvising a volley of them – and it’s arguably better suited to the ringside atmosphere the UK Pun Championships hopes to stoke.

The other flaw in the format is that there’s zero engagement with what makes a pun good or bad. Brodkin cheerfully adjudicates on who wins or loses each bout, but not once does he pull a contestant up for an unnecessary word; or for a weak set-up that undermines the punning punchline; or for over-relying on the same punnable word – as defending champ Leo Kearse does on the word “throne” in the royalty round. (Nor is anyone penalised for joking off topic, which they should be.)

No effort is made, either, to distinguish between or celebrate different types of pun, from the ruthlessly economic nuggets of both Richard Woolford (“Bakers, eh? They’re so kneady!”) and runner-up Richard Pulsford (“Sent a food parcel to my first wife: Fed Ex”) to the less pure sexual innuendoes that Graham makes his own. (I’m not sure his anal sex gag qualifies as a pun at all.)

I’m not asking for a lecture, but it’d be a bonus if the UK Pun Championships demonstrated some feel for what makes punning a skill, for how small its margin for error is, for how it bends minds as well as words. In the absence of that, small wonder the audience roots not necessarily for the best wordsmiths, but the ones who best combine wordsmithery with performing ability and charm. One lesson we are all reminded of tonight: being good at puns isn’t the same as being good at performing, and some capable word-twisters fall at the first hurdle because they can’t sell the gags well on stage.

Graham is a worthy winner. His puns vary more dramatically in quality than Pulford’s, but the best of them are very good: “My English teacher recently recovered from a bowel cancer operation … and he tried to show me a semi colon.” His lackadaisical, ambivalent charisma is eye-catching. He’s right, too, that it’s good to have an event that celebrates the maligned art of wordplay – even if, in its third year, it’s not celebrating that art quite as effectively as it might.

Three to see

Frank SkinnerA week’s work-in-progress for a new experiment, called The Man With No Show, in which one of the nation’s favourite comics takes to the stage with no prepared material whatsoever. •Soho theatre, until 13 February.

Tar BabyThe winner of the Funny Women 2015 crown, American performer Desiree Burch hits the capital with her much discussed comedic solo theatre show about race in the US. •Vault festival, London, 10-14 February.